I have a 50 and a 200 day moving average set up on my chart. For example, on a week chart, I can see the lines cross over, but when I switch to a one or three month chart, I no longer see the lines cross over.  Shouldn't they be the same regardless of what time period I am looking at on the chart since they are referencing a set historical period in time?

The moving averages are based on the time frame of the chart. So you are plotting a 50 period moving average and a 200 period moving average which happen to be 50 day and 200 day moving averages in a daily time frame.

When you switch to a monthly chart the moving averages become 50 month and 200 month moving averages instead.